Both are correct, with different meanings. Although they may be used interchangeably in some cases, the essential distinction is that talking TO someone implies a one-way exchange like a lecture or a...
That's alright as long as it makes a couple of noises that sound like little words like up, car and hi. And if it walks its okay its still young. Its not a big deal but just give the docter a little...
'Who is talking' is usually a question, and would be written "Who is talking?" However, if the person talking actually has the name 'Who', then "Who is talking." would be a correct English statement!...